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In everyday life, there are three familiar dimensions (3D) of space: height, width and length. Einstein's general theory of relativity treats time as a dimension on par with the three spatial dimensions; in general relativity, space and time are not modeled as separate entities but are instead unified to a four-dimensional (4D) spacetime. In ...
Some physicists (e.g., John Baez et al.) have speculated that the exceptional Lie groups E 6, E 7 and E 8 having maximum orthogonal subgroups SO(10), SO(12) and SO(16) may be related to theories in 10, 12 and 16 dimensions; 10 dimensions corresponding to string theory and the 12 and 16 dimensional theories being yet undiscovered but would be ...
The Hausdorff dimension is defined for all metric spaces and, unlike the dimensions considered above, can also have non-integer real values. [6] The box dimension or Minkowski dimension is a variant of the same idea.
Its dihedral angle is cos −1 (1/10), or approximately 84.26°. It can also be called a hendecaxennon , or hendeca-10-tope , as an 11- facetted polytope in 10-dimensions. The name hendecaxennon is derived from hendeca for 11 facets in Greek and -xenn (variation of ennea for nine), having 9-dimensional facets, and -on .
The core breakthrough for the 10-dimensional theory, known as the first superstring revolution, was a demonstration by Michael B. Green, John H. Schwarz and David Gross that there are only three supergravity models in 10 dimensions which have gauge symmetries and in which all of the gauge and gravitational anomalies cancel.
starting to feel better about it all. As we talked with friends, some of them became interested, and soon what began as a ridiculous conversation on the first day in January took on a life of its own. In the end nearly a hundred of us went to Paris in two buses, had a great time, and raised thousands of dollars for charity.
In grand unified theories (GUTs), the Standard Model Lie group is considered as a subgroup of a higher-dimensional Lie group, such as of 24-dimensional SU(5) in the Georgi–Glashow model or of 45-dimensional Spin(10) in the SO(10) model. Since there is a different elementary particle for each dimension of the Lie group, these theories contain ...
In higher dimensions, it is best known for its role in the AdS/CFT correspondence, which suggests that it is possible to describe a force in quantum mechanics (like electromagnetism, the weak force or the strong force) in a certain number of dimensions (for example four) with a string theory where the strings exist in an anti-de Sitter space ...